倍增法求最近公共祖先

Author: Dev-XYS

Lowest-Common-Ancestor(Doubling).cpp

@@ -0,0 +1,101 @@
+#include <cstdio>
+
+using namespace std;
+
+struct vertex
+{
+	int first, depth;
+}V[100010];
+
+struct edge
+{
+	int endp, next;
+}E[200010];
+
+int ec = 1, ivc;
+int fa[100010][25];
+
+void add_edge(int u, int v)
+{
+	E[ec].next = V[u].first;
+	V[u].first = ec;
+	E[ec].endp = v;
+	ec++;
+}
+
+void DFS(int u, int prev, int depth)
+{
+	if (fa[u][0] == 0)
+	{
+		fa[u][0] = prev;
+		V[u].depth = depth;
+		for (int cur = V[u].first; cur != 0; cur = E[cur].next)
+		{
+			DFS(E[cur].endp, u, depth + 1);
+		}
+	}
+}
+
+void init()
+{
+	DFS(1, -1, 1);
+	for (int i = 1; i <= 20; i++)
+	{
+		for (int j = 1; j <= ivc; j++)
+		{
+			fa[j][i] = fa[fa[j][i - 1]][i - 1];
+		}
+	}
+}
+
+int lca(int a, int b)
+{
+	if (V[b].depth > V[a].depth)
+	{
+		int temp = a;
+		a = b;
+		b = temp;
+	}
+	int delta = V[a].depth - V[b].depth, k = 0;
+	while (delta > 0)
+	{
+		if ((delta & 1) == 1)
+		{
+			a = fa[a][k];
+		}
+		k++;
+		delta >>= 1;
+	}
+	if (a == b)
+	{
+		return a;
+	}
+	for (int i = 20; i >= 0; i--)
+	{
+		if (fa[a][i] != fa[b][i])
+		{
+			a = fa[a][i];
+			b = fa[b][i];
+		}
+	}
+	return fa[a][0];
+}
+
+int main()
+{
+	int u, v;
+	scanf("%d", &ivc);
+	for (int i = 1; i < ivc; i++)
+	{
+		scanf("%d%d", &u, &v);
+		add_edge(u, v);
+		add_edge(v, u);
+	}
+	init();
+	while (true)
+	{
+		scanf("%d%d", &u, &v);
+		printf("%d\n", lca(u, v));
+	}
+	return 0;
+}